Über das Buch

Beschreibung

This book will be useful to scientists and engineers who want a simple introduction to the finite volume method. A series of computer codes
are given on the companion website along with worked solutions to exercises. This book is a companion text to 'Introductory Finite Difference Methods for PDEs'.

Einleitung

This material is taught in the BSc. Mathematics degree programme at the Manchester Metropolitan University, UK. The Finite Volume Method (FVM) is taught after the Finite Difference Method (FDM) where important concepts such as convergence, consistency and stability are presented. The FDM material is contained in the online textbook, ‘Introductory Finite Difference Methods for PDEs’ which is free to download from this website

It is recommended that the FDM text book is read before this book. This textbook is also freely downloadable from the above website.

The following chapters contain core material supported by pen and paper exercises together with computer-based exercises where appropriate. Supporting material, including worked solutions, and computer codes can be found at the companion website:

Codes, with which the student can experiment, are written using Matlab. In the spirit of Open Source, it is hoped to reproduce these codes using Scilab (a Matlab clone, downloadable for free from www.scilab.org).

The emphasis of this book is on a practical understanding of the basics of the FVM and a minimum of theory is given to underpin the method. Revision material is provided in appendices. It is recommended that anyone wishing to use the FVM to solve systems of equations for real world applications reads up on the underlying physics of the problem.

This book is intended for final year undergraduates who have knowledge of Calculus, vectors and introductory level computer programming.

Inhalt

Introduction

Introduction

Obtaining the Integral Form from the Differential Form

Finite Volume Meshes

Discretising the Semi-Integral Equation

Implementation

Finite Volume Schemes

Introduction

FVM on a Cartesian Mesh

Finite Volume Schemes in 1D and 3D

Time Step Calculation for a Finite Volume Scheme

Finite Volume FOU 2D Scheme

Boundary Conditions

Coding a Finite Volume Solver

Derivation of Equations

Introduction

Conservation Laws

Control Volume Approach

Deriving the Integral Form of the 2D Linear Advection Equation

Deriving the Differential Form of the 2D Linear Advection Equation

Further Finite Volume Schemes

Introduction

Linear Interpolation

Quadratic Interpolation

Converting from Finite Difference to Finite Volume

Systems of Equations

Introduction

The Shallow Water Equations

General FVS for the SWE

FVS for the 2D SWE on a Structured Mesh

Heuristic Time Step for a 2D SWE FVS

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